Exporting a single plane (floor in this case) as .fbx just with a changed color in Principled BSDF works. However, for my ring which has an image texture for color, metallic and roughness exporting as .fbx shows just model without texture. I put Path Mode to Copy and check Embed Textures. Does it need to be baked or something to be properly exported and shown?
EDIT However, it seems it is possible to export with materials packed into the FBX Exporter. Make sure that there aren't any excess nodes connected to your principled shader (Color Ramp, etc.) From my tests it seems like it will only accept textures connected directly into their corresponding Principled shader input. It won't work with AO mixed with the base color, it won't work with height plugged into the displacement input.
Then in the FBX Exporter change this setting to Copy.
This will create a .fbm folder that will bundle the textures along with it.
After that it seems to work.
Result in UE4.
I think if I had then file naming correct it would have auto-generated the material but anyways.